I've elaborated on this before, but I think 09 has two through lines in it. The first is the importance of father figures and mentors to make great men. Pike for Kirk (and Kirk Sr. to Prime Kirk) and Sarek for Spock. The second is the danger of allowing the darkness to consume you, which is a little more generic. We get these pictures in Nero for Spock and Marcus for Kirk. It's nice because we actually get to see what the darker side could potentially look like. But, I think the fathers' one is the preeminent, and the more important one.
That isn't social commentary, those are bromides. "Don't be evil" is so diluted of all context as to be meaningless.
Also, ST09 doesn't point out the necessity of fatherhood anyway. If anything, the moral of ST09 is that you'll never find your place in the world until your father dies. And then your adopted father figure gets maimed. After that, you're good. Which makes for a messed up message, because you're trying to contrive meaning from mindless fluff.
Nemesis isn't doing social commentary even when it asks its own variation on the nature v nurture argument.
Beyond, despite touching the dangers of losing one's self in the wilderness, didn't offer a lick of social commentary. It throws peans towards antiempiralism and unity, but that's not social commentary. It's more fluff.
Into Darkness and Insurrection did offer social commentaries, albeit in ham fisted ways. Social commentary is, explicitly, commenting on issues which affect societies. ST09, STB are more about issues affecting individuals.
And no, just because society is made up of individuals does not make everything into social commentary.